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on if the state tem is consistent, removing one of it

on if the state tem is consistent, removing one of it

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For each of the following statements, clearly state if it is true or false. Moreover, provide either a counterexample if the statement is false or a brief justification if the statement is true. (i) If a system is consistent, removing one of its equation results in a new system that is inconsistent. (ii) If the columns of an m xn matrix span R", adding one more column to the matrix results in a matrix whose columns span Rm. (iii) If u, v are linear dependent vectors in R“, then u, 2u – v are linearly dependent. (iv) If a system of linear equations has two different solutions, it must have infinitely many solutions.
Transcribed Image Text:For each of the following statements, clearly state if it is true or false. Moreover, provide either a counterexample if the statement is false or a brief justification if the statement is true. (i) If a system is consistent, removing one of its equation results in a new system that is inconsistent. (ii) If the columns of an m xn matrix span R", adding one more column to the matrix results in a matrix whose columns span Rm. (iii) If u, v are linear dependent vectors in R“, then u, 2u – v are linearly dependent. (iv) If a system of linear equations has two different solutions, it must have infinitely many solutions.
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